Question: Simplify the following expression: $\dfrac{20x^4}{12x}$ You can assume $x \neq 0$.
Solution: $ \dfrac{20x^4}{12x} = \dfrac{20}{12} \cdot \dfrac{x^4}{x} $ To simplify $\frac{20}{12}$ , find the greatest common factor (GCD) of $20$ and $12$ $20 = 2 \cdot 2 \cdot 5$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(20, 12) = 2 \cdot 2 = 4 $ $ \dfrac{20}{12} \cdot \dfrac{x^4}{x} = \dfrac{4 \cdot 5}{4 \cdot 3} \cdot \dfrac{x^4}{x} $ $\phantom{ \dfrac{20}{12} \cdot \dfrac{4}{1}} = \dfrac{5}{3} \cdot \dfrac{x^4}{x} $ $ \dfrac{x^4}{x} = \dfrac{x \cdot x \cdot x \cdot x}{x} = x^3 $ $ \dfrac{5}{3} \cdot x^3 = \dfrac{5x^3}{3} $